Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 109
... reduces to the conventional - Lf ( r ) = g ( r ) ( ordinary or partial ) differential equation D ( r ) f ( r ) = g ( r ) Similarly , the equation a f ( r , t ) = Lf ( r , t ) Ət a reduces to f ( r , t ) = D ( r ) f ( r , t ) Ət It is ...
... reduces to the conventional - Lf ( r ) = g ( r ) ( ordinary or partial ) differential equation D ( r ) f ( r ) = g ( r ) Similarly , the equation a f ( r , t ) = Lf ( r , t ) Ət a reduces to f ( r , t ) = D ( r ) f ( r , t ) Ət It is ...
Página 139
... reduces to or wx Σ infn , 1 n = -∞ + ∞ eix = eir co COS = + ∞ eir cos e = Σ inJn ( r ) eino ( 10.40 ) n = -∞ By equating the real and imaginary parts of both sides of ( 10.40 ) it is found that and cos ( r cos 0 ) = Jo ( r ) + 2 Σ i ...
... reduces to or wx Σ infn , 1 n = -∞ + ∞ eix = eir co COS = + ∞ eir cos e = Σ inJn ( r ) eino ( 10.40 ) n = -∞ By equating the real and imaginary parts of both sides of ( 10.40 ) it is found that and cos ( r cos 0 ) = Jo ( r ) + 2 Σ i ...
Página 205
... reduces to σ ( 8L ) f + L df = ( 82 ) £ ̧ + 2 ̧ df One now seeks a left multiplier such that the terms Ldf2 , df = ( L — 2 ̧ ) df ( 14.15 ) are annihilated . Use gt such that - g + ( L — λ ) = 0 and obtain or g + ( 8L ) f = g + ( 82 ) f ...
... reduces to σ ( 8L ) f + L df = ( 82 ) £ ̧ + 2 ̧ df One now seeks a left multiplier such that the terms Ldf2 , df = ( L — 2 ̧ ) df ( 14.15 ) are annihilated . Use gt such that - g + ( L — λ ) = 0 and obtain or g + ( 8L ) f = g + ( 82 ) f ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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approximate arbitrary ax² basis Bessel function boundary conditions chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined denoted determinant diagonal differential equation Dirac notation domain eigen eigencolumns eigenfunctions eigenvalue equation eigenvector eikr evaluate expansion finite number follows Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplace transform Laplacian linear operator linearly independent lowest eigenvalue matrix membrane method multiplication nonsingular normal obtained orthonormality conditions plane problem procedure relations representation result satisfies the boundary scattering sinh solve spherical spherical harmonics string Substitution theorem trial functions vanish variable vector space Verify wave write written y₁ yields York zero ηπχ πο ποχ ди ду дх